AMERICA’S new health law would bring change, Democrats said, but not too much. In the battle over Obamacare, no matter was more delicate than the fear that Americans would lose their insurance. “If you like your health care plan,” Barack Obama assured a town-hall meeting in 2009, “you can keep your health care plan.”

Two years later, the debate continues. The basic question is whether America will abandon the current system of employer-sponsored health care in favour of insurance offered through state exchanges. A new survey from the National Federation of Independent Business (NFIB) suggests that it might.

The law certainly makes the switch tempting. Under reform, all companies with more than 50 workers must offer health benefits to every full-time employee or pay a penalty of $2,000 per worker. The health law creates new requirements for the benefits that must be covered. Meanwhile the unemployed, the poor and workers who are not offered affordable care through their employers will receive subsidies for buying insurance on newly created “exchanges”.

Faced with these changes, workers and employers will think about health care rather differently. For an employer, the $2,000 penalty will probably work out cheaper than offering health insurance that meets all the new requirements. For many workers, the subsidies they will get from the exchanges will far exceed any tax benefits from employer-sponsored insurance, according to Eugene Steuerle of the Urban Institute.

NFIB’s survey of 750 small employers assumes that many poor workers will prefer the exchanges’ subsidies—it is a simple matter of logic. These workers’ decisions will affect those who prefer to stick with their existing health plans. If some employees leave for the exchanges, NFIB found, 57% of firms would be “somewhat” or “very likely” to consider dropping insurance completely.

The report bolsters the results of another survey, published by McKinsey last month. McKinsey’s report found that 30% of firms would definitely or probably stop offering insurance after 2014, when the exchanges are in place. The Congressional Budget Office had estimated a much lower share, just 7%. The report sparked a political explosion. McKinsey, which usually contorts itself to stay out of the news, became a headline regular. Republicans issued I-told-you-so press releases. Democrats were apoplectic. Max Baucus, a senator, sent the consultancy a furious letter. “This one flawed study from McKinsey is truly an outlier,” wrote Nancy-Ann DeParle, Mr Obama’s deputy chief of staff.

Democrats have reason to be anxious. Not only do the surveys undermine Mr Obama’s claim that Americans can keep their insurance if they like: they also suggest that the exchanges’ subsidies will gobble up more money than expected. There is at least one factor preventing a migration to exchanges, though it will not give Democrats much solace. State governments are making dismal progress towards creating exchanges. The migration to the exchanges in 2014 will not happen if they do not exist.